Lesson 8 Menu : Lesson 8 Menu Five-Minute Check (over Lesson 6-7)
Main Ideas and Vocabulary
California Standards
Example 1: Solve By Graphing
Example 2: Use a System of Inequalities
Lesson 8 MI/Vocab : Lesson 8 MI/Vocab system of inequalities Solve systems of inequalities by graphing. Solve real-world problems involving systems of inequalities.
Lesson 8 CA : Lesson 8 CA Standard 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. (Key, CAHSEE)
Lesson 8 Ex1 : Lesson 8 Ex1 Solve By Graphing A. Solve the system of inequalities by graphing.
y < 2x + 2
y ≥ – x – 3 Answer: The solution includes the ordered pairs in the intersection of the graphs of y < 2x + 2 and y ≥ – x – 3. The region is shaded in green. The graphs y = 2x + 2 and y = – x – 3 are boundaries of this region. The graph y = 2x + 2 is dashed and is not included in the graph of y < 2x + 2. The graph of y = – x – 3 is included in the graph of y ≥ – x – 3. Animation: Solving Systems of Equations by Graphing
Lesson 8 Ex1 : Lesson 8 Ex1 Solve By Graphing B. Solve the system of inequalities by graphing.
y ≥ –3x + 1
y ≤ –3x – 2 Answer: The graphs of y = –3x + 1 and y = –3x – 2 are parallel lines. Because the two regions have no points in common, the system of inequalities has no solution.
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D A. Solve the system of inequalities by graphing 2x + y ≤ 4 and x + y > –4.
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D B. Solve the system of inequalities by graphing.y > 4xy < 4x – 3
Lesson 8 Ex2 : Lesson 8 Ex2 SERVICE A college service organization requires that its members maintain at least a 3.0 grade point average, and volunteer at least 10 hours a week.Graph these requirements. Words The grade point average is at least 3.0. The number of volunteer hours is at least 10 hours. Variables If g = the grade point average and v = the number of volunteer hours, the following inequalities represent the requirements of the service organization. Use a System of Inequalities
Lesson 8 Ex2 : Lesson 8 Ex2 Inequalities The grade point average is at least 3.0. g ≥ 3.0 Answer: The solution is the set of all ordered pairs whose graphs are in the intersection of the graphs of these inequalities. Use a System of Inequalities The number of volunteer hours is at least 10. v ≥ 10
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D The senior class is sponsoring a blood drive. Anyone who wishes to give blood must be at least 17 years old and weigh at least 110 pounds. Graph these requirements.
End of Lesson 8 : End of Lesson 8